Problem

e. tickets for a basketball game cost $\$ 2$ for students and $\$ 5$ for adults. The number of students was 3 less than 10 times the number of adults. The total amount of money from ticket sales was $\$ 619$. How many of each ticket were sold?

Answer

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Answer

Final Answer: The number of adult tickets sold was \(\boxed{25}\) and the number of student tickets sold was \(\boxed{247}\).

Steps

Step 1 :Let's denote the number of student tickets as \(s\) and the number of adult tickets as \(a\).

Step 2 :We can then set up the following equations based on the problem:

Step 3 :1) \(2s + 5a = 619\) (This is based on the total amount of money from ticket sales)

Step 4 :2) \(s = 10a - 3\) (This is based on the number of students being 3 less than 10 times the number of adults)

Step 5 :We can then solve this system of equations to find the values of \(s\) and \(a\).

Step 6 :The solution to the system of equations is \(\{a: 25, s: 247\}\). This means that 25 adult tickets and 247 student tickets were sold.

Step 7 :Final Answer: The number of adult tickets sold was \(\boxed{25}\) and the number of student tickets sold was \(\boxed{247}\).

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